A rectangle is 3 miles longer than it is wide. Find the dimensions of the rectangle if it’s area is 247 sq-miles

Question

Enter your answer as an expression to be calculated

Answer 1

If we let L= length and W=width and A = area=(LxW)

thenL=W+3 so the area A=(W+3)(W)=W²+3W=247 which is a quadratic equation

W²+3W-247=0 The positive root gives the width adding 3 gives the length, I gotW=14.29 and L=17.29

Jim

Answer 2

Since we are given the dimensions of this rectangle as a means of one variable (its width), we can build a model using the known area of a rectangle to help us find the solution...

A_rect = Length x Width

Width = w [ we aren't given this information so it is an unknown variable ]

Length = 3 + w [ we are given this information in the problem ]

A_rect = (3 + w)(w) = 3w + w²

Now, the total area provided by the problem is 247 sq-miles ( the total area )

A_rect = 247 = 3w + w²

So we employ the quadratic formula to help us solve this...

247 = 3w + w²

w² + 3w - 247 = 0

w = ( -3 +/- sqrt[32 - 4(-247)(1)] ) / 2

w = ( -3 +/- sqrt(1020) ) / 2

w ≈ ( - 3 +/- 31.9 ) / 2

w ≈ 14.45 or w ≈- -17.45

Since the length, width, and area are strictly positive quantityies, we can safely throw away the negative width solution.

Answer 3

Let us call the length of the rectangle x, and the width of the rectangle is y.

Since the area of the rectangle is length * width, we know that

Area = x*y;

x*y = 247

The other thing we know is that one side is 3 miles longer than the other.

y = x +3;

Now we have two equations two unknowns.

x*y = 247

y = x+3

Substitute the value of y in the second equation into the first one.

Then just solve and you're done!

x*(x+3) = 247

From there you should be able to find the dimensions by solving for x and plugging into x+3.